What you need is a HDMI switch (not a splitter). Your projector isn't a 'source' for your system, your SOURCES are the sources for the system. PS5, cable box, Roku, laptop, PC, etc... All those would connect to a HDMI switch, then you would switch between your sources, and pass audio out to your receiver.

A proper HDMI switch with audio extractor is readily available. You want one that is rated for 18Gb/s HDMI. That is 60 frames per second, plus HDR support.

This is one of MANY on Amazon...
https://www.amazon.com/ROOFULL-Optical-Extractor-Splitter-Support/dp/B095H9NF35/ref=sr_1_3

Search for "HDMI Switch Audio Extractor" and you will see there are tons of results. You want one which calls out HDMI 2.0 (or better) and claims 18Gbs somewhere in the description as well.